广义对称正则长波方程的孤波解和周期波解及它们与Hamilton能量的关系

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 603-628.

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Periodic Wave Solutions, Solitary Wave Solutions and Their Relationship for Generalized Symmetric Regularized Long Wave Equation with Two Nonlinear Terms

Xingqian Ling¹(),Weiguo Zhang^2,*()

¹ Business School, University of Shanghai for Science and Technology, Shanghai 200093
² College of Science, University of Shanghai for Science and Technology, Shanghai 200093

Received:2020-06-12 Online:2021-06-26 Published:2021-06-09
Contact: Weiguo Zhang E-mail:1097576100@qq.com;zwgzwm@126.com
Supported by:
the NSFC(11471215)

Abstract

Abstract:

In this paper, we study the exact solitary wave, periodic wave solutions and their evolutionary relationship with Hamilton energy for generalized symmetric regularized long wave equation. By the planar dynamical system method, we make detailed qualitative analysis on this equation. Then we use the first integral method to obtain the exact solutions for the equation. Furthermore, by establishing the corresponding relationships between the solitary wave, periodic wave solutions and Hamilton energy h, we reveal that the value of Hamilton energy h plays an important role in the appearance of solitary wave and periodic wave solutions. The evolution processes from the periodic wave solution to the solitary wave solution and the kink wave solution are also given in this paper.

Key words: Generalized symmetric regularized long wave equation, Planar dynamical system, Solitary wave solution, Periodic wave solution, Evolutionary relationship

CLC Number:

O175.2

Xingqian Ling,Weiguo Zhang. Periodic Wave Solutions, Solitary Wave Solutions and Their Relationship for Generalized Symmetric Regularized Long Wave Equation with Two Nonlinear Terms[J].Acta mathematica scientia,Series A, 2021, 41(3): 603-628.

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References

1	Seyler C F , Fenstermmacher D C . A symmetric regularized long wave equation. Phys Fluids, 1984, 27 (1): 4- 7
2	Bogolubsky I L . Cascade evolution of spherically symmetric pulsons in multivacuum field theory models. Phys Lett A, 1977, 61 (4): 205- 206
3	Makhankov V G . Dynamics of classical solitons (in non-integrable systems). Phys Rep, 1978, 35 (1): 1- 128
4	Ogino T , Takeda S . Computer simulation and analysis for the spherical and cylindrical ion-acoustic solitons. J Phys Soc, 1976, 41, 257- 264
5	Miao C X . The initial boundary value problem for symmetric long wave equations with nonhomogeneous boundary value. Northeastern Math J, 1994, 10 (4): 463- 472
6	Dereli Y , Ayse G . Numerical solutions of the symmetric regularized long wave equation using radial basis functions. Comp Model Eng, 2012, 84 (5): 423- 438
7	Khater M , Abdelrahman M . Traveling solitary wave solutions for the symmetric regularized long-wave equation. Adv Math, 2015, 11 (8): 5520- 5528
8	Manafian J , Zamanpour I . Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods. Stat Optim Inf Comput, 2014, 2, 47- 55
9	Lu D C , Seadawy A R , Asghar A . Applications of exact traveling wave solutions of modified Liouville and the symmetric regularized long wave equations via two new techniques. Results Phys, 2018, 9, 1403- 1410
10	Zhao X . An exponential wave integrator pseudospectral method for the symmetric regularized-long-wave equation. J Comput Math, 2016, 34 (1): 49- 69
11	Yavuz U , Dogan K , Ibrahim E I . Generalized Jacobi elliptic function method for periodic wave solutions of SRLW equation and (1+1)-dimensional dispersive long wave equation. Cam Univ J Sci Eng, 2011, 7, 39- 50
12	尚亚东. 具5次强非线性项的广义对称正则长波方程的显式精确解. 石油化工高等学校学报, 1999, 4, 85- 89
12	Shang Y D . Precise and explicit solutions to a generalized symmetric regularized long wave equations with five order stronger nonlinear term. J Petr Univ, 1999, 4, 85- 89
13	Zhang W G , Chen X , Li Z , et al. Orbital stability of solitary waves for generalized symmetric regularized-long-wave equations with two nonlinear terms. J Appl Math, 2014, 2014 (1): 1- 16
14	Nemytskii V , Stepanov V . Qualitative Theory of Differential Equations. New York: Dover, 1986
15	Zhang Z F , Ding T R , Huang W Z . Qualitative Theory of Differential Equations. Providence RI: American Mathematical Society, 1992
16	Byrd P F , Friedman M D . Handbook of Elliptic Integrals for Engineers and Scientists. New York: Springer, 1971
17	Lawden D F . Elliptic Functions and Applications. New York: Springer, 1989

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Periodic Wave Solutions, Solitary Wave Solutions and Their Relationship for Generalized Symmetric Regularized Long Wave Equation with Two Nonlinear Terms

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